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Hello,

Apologies for this very basic question, but I was wondering if someone could confirm whether or not interactions between design attributes and covariates impact the degrees of freedom calculation, and hence the number of choice tasks needed in the study design.

At the moment, I assume that only interactions between design attributes impact the minimum required number of degrees of freedom, and that interactions between design attributes and sociodemographic covariates are inconsequential to the degrees of freedom calculation.

Many thanks,
Stephen

Hi Stephen

From a design perspective, only design related parameters are used in the calculation. The degrees of freedom required is pure and simple a matrix inversion issue. Despite how the design is outputted, Internally the design format is such that each row is an alternative, J, not a choice set S, and hence several rows are grouped together to form a choice set. This means that in the calculations, the number of rows for the entire design is S*J. To invert the hessian in order to calculate the AVC matrix, the number of rows needs to be equal to or greater than the number of columns, K, which are the attributes (parameters). So unless you have socio-demographic parameters directly accounted for when generating the design, these are ignored in the calculation. Should you account for them - theoretically yes - you want to mimic the AVC matrix you are going to get at the end of the day as closely as possible which may include socio-demographics. In practice, this is very difficult to do when generating the design, so aside from one paper we wrote for a conference, it hasn't been done to the best of my knowledge.

John

johnr wrote:@expert
Hi Stephen

From a design perspective, only design related parameters are used in the calculation. The degrees of freedom required is pure and simple a matrix inversion issue. Despite how the design is outputted, Internally the design format is such that each row is an alternative, J, not a choice set S, and hence several rows are grouped together to form a choice set. This means that in the calculations, the number of rows for the entire design is S*J. To invert the hessian in order to calculate the AVC matrix, the number of rows needs to be equal to or greater than the number of columns, K, which are the attributes (parameters). So unless you have socio-demographic parameters directly accounted for when generating the design, these are ignored in the calculation. Should you account for them - theoretically yes - you want to mimic the AVC matrix you are going to get at the end of the day as closely as possible which may include socio-demographics. In practice, this is very difficult to do when generating the design, so aside from one paper we wrote for a conference, it hasn't been done to the best of my knowledge.

John

Hi John,

Is the paper you mentioned available in a free online access? I would appreciate any link to the conference materials too, if possible. I'm searching for the calculation methods for the safety and effectiveness parameters in case of specific alternatives (for my DCE research project).

Thanks,
Renee

Hi Stephen
I'm not sure about free online. If you drop me an email, I can send you a word version. We discuss this in a few articles but the one that comes most immediately to mind is

Rose, J.M. and Bliemer, M.C.J. (2014) Stated choice experimental design theory: The who, the what and the why, in Hess, S. and Daly, A. (eds.) Handbook of Choice Modelling, Edward Elgar, Cheltenham, 152-177.

The conference article was

Rose, J.M. and Bliemer, M.C.J. (2006) Designing Efficient Data for Stated Choice Experiments, 11th International Conference on Travel Behaviour Research, Kyoto, August 16-20, 2006, Japan.

John